Radiation transport theory is applied to electron microscopy of samples composed of one or more materials. The theory, originally due to Goudsmit and Saunderson, assumes only elasticscattering and an amorphous medium dominated by atomic interactions. For samples composed of a single material, the theory yields reasonable parameter-free agreement with experimental data taken from the literature for the multiple scattering of electrons through aluminum foils up to thick. For thin films, the theory gives a validity condition for Beer’s law. For thick films, a variant of Molière’s theory [V. G. Molière, Z. Naturforschg.3a, 78 (1948)] of multiple scattering leads to a form for the bright-field signal for foils in the multiple-scattering regime. The signal varies as where is the path length of the beam, is the mean free path for elasticscattering, and is Euler’s constant. The Goudsmit–Saunderson solution interpolates numerically between these two limits. For samples with multiple materials, elemental sensitivity is developed through the angular dependence of the scattering. From the elasticscattering cross sections of the first 92 elements, a singular-value decomposition of a vector space spanned by the elasticscattering cross sections minus a delta function shows that there is a dominant common mode, with composition-dependent corrections of about 2%. A mathematically correct reconstruction procedure beyond 2% accuracy requires the acquisition of the bright-field signal as a function of the scattering angle. Tomographic reconstructions are carried out for three singular vectors of a sample problem with four elements Cr, Cu, Zr, and Te. The three reconstructions are presented jointly as a color image; all four elements are clearly identifiable throughout the image.

We examine the optical properties of three-dimensional metallic photonic crystals made from a periodic stacking of thin metallic mesh layers separated by homogeneous dielectric films by means of a combination of the plane-wave-based transfer-matrix method and analytical modal solution approach. Although each metallic mesh layer can serve as a frequency-selective surface and involves an intrinsic long-wavelength waveguide cutoff to electromagnetic waves, pass bands and new band gaps can exist far below the cutoff frequency due to the global coupling effect among different mesh layers. The results for the transmission spectra and photonicband structures are in good agreement with existing experimental measurements. It is found that the position of the pass bands and band gaps strongly depends on the thickness and composite of the separation layer between the adjacent metallic mesh layers.

Photonic crystal fibers guide light by trapping it in a periodic array of elements in the cladding area. We fabricatedphotonic crystal fibers by multiple extrusions of silver halide crystals which are highly transparent in the middle infrared. The core of such a fiber consisted of pure silver bromide AgBr ( at ), and the cladding area consisted of concentric rings of fiber-optic elements made of pure silver chloride AgCl ( at ), which lowered the refractive index of the clad. Two types of photonic crystal fibers were fabricated, one with two concentric rings and one with five concentric rings of fiber-optic elements around the core. The characterization of the fibers, such as the power distribution, the attenuation, and the numerical aperture were measured. Both fibers behaved like regular core-clad structures. Simulations on these structures showed that each of these fibers guided a small number of modes and that adding rings to the structure lowered the number of bound modes in the core. This would pave the way for the fabrication of single-mode fibers. Photonic crystal fibers offer many advantages compared to conventional fibers, and they will be extremely useful for many applications in the middle and far infrared.